Computation of near-minimum-time maneuvers of flexible structures by parameter optimization

Abstract

Near-minimum-time attitude maneuvers of space structures as well as ground-based test articles are consid- ered. The switching nature of the controls for rigid-body maneuvers is illustrated using a control cube and a crit- ical control axis. The presence of torque smoothing and, where appropriate, gravitational effects and connections to other bodies are explicitly included in the mathematical models of the systems to be optimized. A maximum fuel consumption constraint is included along with the required terminal conditions on attitude and angular velocities. The switch times, maximum thrust magnitudes, and smoothing parameters are determined using the sequential quadratic programming method for parameter optimization. Results indicating attitude and angular velocity histories, thruster forces, and structural vibrations are presented for three, four, and five switch maneu- vers, as well as maneuvers that involve large coasting arcs. A variety of performance indices based on torque, power, and time have been considered. Except for Refs. 12 and 13, applications to flexible spacecraft models have been limited to single-axis maneuvers. A recent survey article on time-optimal attitude maneuvers is pre- sented in Ref, 18. Solution to the optimization problem usually proceeds by invoking Pontryagin's principle, which leads to a two- point boundary-value problem (TPBVP).19 This is solved using either direct (gradient) or indirect (shooting) methods. The switch- time optimization algorithm (STO)20 is a direct method available for the solution of time-optimal control problems. Adaptation of a shooting method to solve time-optimal maneuver problems is given by Li and Bainum.21 Bilimoria and Wie22 considered the specific problem of time- optimal control of a sphere with three orthogonal control inputs, each bounded by ±1. They also restricted their attention to attitude boundary conditions that could otherwise be achieved by single- axis rotations about an Euler axis. Their results show that Euler- axis rotations are not time optimal in general; there are two types of switching sequences: five switches for rotation angles greater than 73 deg and seven switches for angles less than 73 deg. The switches are sequential, i.e., no control switches for the second time before all others switch. Li and Bainum21 present results for rest-to-rest maneuvers of nearly symmetric spacecraft that show similar behavior. However, for highly unsymmetric spacecraft and arbitrary attitude boundary conditions, the number and sequence of switches are not predictable as they are for spherical bodies. Byers and Vadali23 and Byers et al.24 used the STO algorithm to compare the Euler-axis, five-switch, and seven-switch maneuvers for Euler- axis boundary conditions and found that the differences in the maneuver times are insignificant for practical implementations. A suboptimal control strategy was developed in Ref. 23 by assuming a five-switch control sequence and an approximate solution to the Euler parameter differential equation. This switching structure also